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authorHolden Rohrer <hr@hrhr.dev>2020-04-14 22:42:59 -0400
committerHolden Rohrer <hr@hrhr.dev>2020-04-14 22:42:59 -0400
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@@ -78,6 +78,15 @@ should be a particular solution. This would allow usage of method of
undetermined coefficients, which may be attempted, but variation of
parameters will be used so that a general form for both systems with
both complex and real eigenvalues may be found.
+Essentially, the solution is ${\bf x} = c_1{\bf\lambda_1}(t) +
+c_2{\bf \lambda_2}(t) + c_3{\bf \lambda_3}(t){\bf\lambda_p}(t)$,
+where the particular solution ${\bf\lambda_p}(t)$ is:
+$${\bf \lambda_p}(t) = {\bf X}(t)\int{\bf X^{-1}}(t){\bf g}(t)dt,$$
+where $\bf{X}(t)$ is the Fundamental matrix for the equation and
+${\bf g}(t) = {1\over R_1}
+\pmatrix{\omega\cos(\omega t)\cr
+ \omega\cos(\omega t)\cr
+ 0}.$
\section{Possible Generalization}